ISTANBUL, Aug 4 (Reuters) - The PKK, which has spent three decades fighting for autonomy for Turkey's Kurds, on Monday urged all Kurds to take up the fight against the Sunni militants of Islamic State, who have expanded their advance across Iraq into Kurdish-controlled territory.

The Kurds populate an area that extends from southeastern Turkey through northeastern Syria and northern Iraq, into western Iran.

"All Kurds in the north, east, south and west must rise up against the attack on Kurds in Sinjar (in northern Iraq)," the Kurdistan Workers' Party (PKK) said in a statement on its website.

Islamic State inflicted a heavy defeat on Iraq's Kurds on Sunday with a rapid advance through three towns to reach the Mosul Dam, the largest in Iraq and a major source of electricity.

"All Kurdish political powers must take part in this resistance, shoulder-to-shoulder. When Kurds are attacked, they must show the attackers that they will find all Kurds against them," the PKK said.

The PKK, currently engaged in a peace process with the Turkish state, is based in the mountains of northern Iraq but also has fighters in Turkey. It is also allied with rebel Kurdish forces fighting Islamic State in Syria.

Iraq's Prime Minister Nuri al-Maliki has ordered his air force for the first time to back Kurdish forces against the Sunni militant group, according to Iraqi state television. (Writing by Daren Butler; Editing by Nick Tattersall and Kevin Liffey)

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